Solve the equation x^2+3x=0?

Question

Solve the equation x^2+3x=0?

Answer 1

x(x+3)=0

x=0 , -3

Answer 2

x^2 + 3x = 0

x(x + 3) = 0 ----- factor out an x

x = 0

x + 3 = 0

x = -3

x = 0, x = -3

Answer 3

x² + 3x = 0

Factor out x:

x(x + 3) = 0

If the product of 2 terms = 0, then one or both terms = 0.

x = 0, or

x + 3 = 0. or

x = -3

x{0, -3}

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Answer 4

Question Number 1 :

For this equation x^2 + 3*x  = 0 , answer the following questions :

A. Find the roots using Quadratic Formula !

B. Use factorization to find the root of the equation !

C. Use completing the square to find the root of the equation !

Answer Number 1 :

The equation x^2 + 3*x  = 0 is already in a*x^2+b*x+c=0 form.

As the value is already arranged in a*x^2+b*x+c=0 form, we get the value of a = 1, b = 3, c = 0.

1A. Find the roots using Quadratic Formula !

  Remember the formula,

    x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)

  We had know that a = 1, b = 3 and c = 0,

  we need to subtitute a,b,c in the abc formula, with thos values.

  So x1 = (-(3) + sqrt( (3)^2 - 4 * (1)*(0)))/(2*1) and x2 = (-(3) - sqrt( (3)^2 - 4 * (1)*(0)))/(2*1)

  Which is the same as x1 = ( -3 + sqrt( 9+0))/(2) and x2 = ( -3 - sqrt( 9+0))/(2)

  Which make x1 = ( -3 + sqrt( 9))/(2) and x2 = ( -3 - sqrt( 9))/(2)

  It imply that x1 = ( -3 + 3 )/(2) and x2 = ( -3 - 3 )/(2)

  So we have the answers x1 = 0 and x2 = -3

1B. Use factorization to find the root of the equation !

  x^2 + 3*x  = 0

  ( x  ) * ( x + 3 ) = 0

  So we have the answers x1 = 0 and x2 = -3

1C. Use completing the square to find the root of the equation !

  x^2 + 3*x  = 0 ,divide both side with 1

  Then we get x^2 + 3*x  = 0 ,

  The coefficient of x is 3

  We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = 3/2 = 1.5

  Which means we can turn the equation into x^2 + 3*x + 2.25 - 2.25 = 0

  Which can be turned into ( x + 1.5 )^2  - 2.25 = 0

  Which can be turned into (( x + 1.5 ) - 1.5 ) * (( x + 1.5 ) + 1.5 ) = 0

  Which is the same with ( x + 1.5 - 1.5 ) * ( x + 1.5 + 1.5 ) = 0

  Just add up the constants in each brackets, and we get ( x  ) * ( x + 3 ) = 0

  The answers are x1 = 0 and x2 = -3

Answer 5

x^2 + 3x = 0

x(x+3)   = 0

two solutions:

           x= 0

           x= -3